SOLVING EQUATIONS WITH THE GIVEN ROOTS

Problem 1 :

ix³ + 2x² + 1 = 0

If i is one root of the above equation, find the other roots.

Solution :

Problem 2 :

x⁴ - 2x² - 3 = 0

If -√3 and √3 are the two roots of the above equation, find the other roots.

Solution :

Problem 3 :

x³ + 2x² + 9x + 18 = 0

If 3i one root of the above equation, find the other roots.

Solution :

Problem 4 :

x⁴ - 4x³ + 4x² + 36x - 117 = 0

If (2 + 3i) is one root of the above equation, find the other roots.

Solution :

Problem 5 :

Show that 2a is a root to the equation given below.

x³ + (4 - a)x² - 2(2a + a²)x = 8a²

Solution :

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